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Some basic problems of the mathematical theory of elasticity
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The article was published on 1953-01-01 and is currently open access. It has received 6106 citations till now. The article focuses on the topics: Elasticity (economics) & Mathematical theory.read more
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The mathematical theory of equilibrium cracks in brittle fracture
TL;DR: In this paper, the authors present a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discuss the results obtained thereby, and the object of the theory is the study of the equilibrium of solids in the presence of cracks.
Journal ArticleDOI
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
Journal ArticleDOI
Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour
TL;DR: In this article, the main overall elastic moduli of fiber composites with transversely isotropic phases are connected by simple universal relations which are independent of the geometry at given concentration.
Journal ArticleDOI
Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure
H. Horii,Sia Nemat-Nasser +1 more
TL;DR: In this paper, the elasticity boundary value problem associated with cracks growing from the tips of a model flaw is solved, and the variations of the "ultimate strength" and the orientation of the overall fault plane with confining pressure are estimated.